MAT 2384 Study Guide - Final Guide: Radioactive Decay, Linear Algebra, Diagonalizable Matrix

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 2384
• Professor: Steve Desjardins

Document Summary

Mass-spring system: mx = kx (k > 0) Radioactive decay: n (t) = kn (t) (k > 0: check that a given function is a solution of the ode: Y(x) = e 3x solution of y = 3y. X(t) = cos(2t) sin(2t) solution of the mass-spring equation x = 4x: course objectives (ode part) Understand what is an ode, and what is a solution of a ode. Classify odes: (1) identify the type of an ode and (2) choose an appropriate solution method. Solve the initial value problem associated with an ode. Lecture 2, september 10: initial value problem. De nition and idea of the theorem of existence and uniqueness: separable odes, examples of separable odes: (y2 + 1)y = x y (with y(1) = 1), y2exy = x(1 + y3) Lecture 3, september 13: equations in di erential forms. 1: example: (3x2 4y2)dx + xydy = 0, with u = y/x and u = x/y, introduction to exact odes.